Team: 1141 10/08/13

PROJECT LOON

The aim of “Project Loon” is to ensure everyone on the planet has

access to the internet, by creating a balloon-powered network.

How many balloons would be required to provide balloon-powered

internet coverage to all of New Zealand?

Summary

Project Loon is being developed by “Google”. It is a research project being constructed in

order to provide internet access to every single person on the planet; especially people

living in isolated areas. Using solar powered balloons placed high in the stratosphere (at an

altitude of around 20Km), a world-wide wireless network is hoped to be achieved. The

ground surface area that each balloon covers has a diameter of 40Km.

We have been asked to find out how many balloons will be needed to provide internet

coverage for the whole of New Zealand.

Our interpretation of the question: We are finding out how many balloons will be needed

over New Zealand at any instant in time for there to be enough internet coverage for

everyone.

The surface area that each balloon provides internet cover for, is circular in shape. This

means that all of the balloons in the stratosphere will have to be close enough together that

their internet signals overlap. Our final number of balloons needed to provide internet for

the whole of New Zealand, reflected on this key idea. After copious amounts of research, we

also found that there would need to be more internet coverage over densely populated

areas such as Auckland and Wellington, than over isolated areas, as the demand for internet

would be larger. This meant that the coverage areas of each balloon would need to overlap

even further over populated areas than isolated areas.

It was decided that every part of the country needed to be covered by internet from at least

four balloons. To achieve this, we overlapped the second balloon to the mid-point of the

first balloon as seen in figure 2. The urban areas needed even more coverage as there would

be greater demands for internet.

After calculating the area of New Zealand and the Chatham islands combined, (combined

area = 417 904.43 Km2), and the surface area of the Urban area of New Zealand, (5078 Km2

(including the Chatham Islands), we found the area of New Zealand that had lower

populations densities. This came out at 412826 Km2. This meant that the number of

balloons needed to cover this area is 1033 balloons. (The working out for this answer is

shown in body paragraphs).

We later found that the number of balloons needed for the more densely populated areas is

51 balloons. This meant that the total number of balloons needed over New Zealand at any

point in time is 1084 balloons (1033 + 51).

Introduction:

The internet: one huge global network consisting of staggering amounts of information

about every topic imaginable. This relatively new invention has changed the face of the

planet forever. For most people in the Western world, the internet is taken for granted. But

for 2/3 of people world-wide, it is something they have to live without. Now, “Project Loon”

is making it possible for everyone to access the internet no matter where you live. Using

solar powered balloons placed high in the stratosphere (at an altitude of around 20Km), a

world-wide wireless network could be achieved. The main problem, is figuring out how

many balloons will need to be ejected into the sky to give internet coverage to every part of

the earth. This document contains the answers.

Interpreting the question: Our team is finding out how many balloons will be needed over

New Zealand at any instant in time for there to be enough internet coverage for everyone.

A few assumptions were made in order to come to an accurate answer. One assumption we

made was based on the fact that the balloons were 20 Km above the earth’s surface. In the

stratosphere, winds are relatively slow moving. They start at speeds of around 8Km per

hour, and can reach wind speeds of 32.2 Km per hour. The prevailing wind travels from

West to East in the Stratosphere, and any balloons in the Stratosphere will be pushed along

by the winds. The problem is that different parts of the stratosphere will have winds

travelling at different speeds.

In order to accurately give the earth proper internet cover, there will need to be balloons

covering the oceans so that when the winds in the stratosphere blow the balloons towards

the East, the balloons that were transmitting internet connection over the oceans would

now be transmitting internet connection over a country.

To ensure that the balloons stay in the correct mesh structure, they all have to move with

the Stratosphere wind at the same rate. The different layers of the stratosphere provide

different wind speeds. In order to keep the balloons travelling around the earth together, it

will be necessary to differ the level at which they travel in order to reduce/ increase their

speed to keep up with the other balloons. To do this, they will need to lower or raise the

balloons within the stratosphere. This is easily achieved. There are two parts to the balloon.

One is dark, and one is light. The solar panels found underneath the balloon are used to

power the rotation of the balloon. When the balloon needs to be raised, the balloon rotates

in order to face the dark side towards the sun. The black colour absorbs the sunlight making

the gases within the balloon expand causing the balloon to rise. This is because the

absorption of sunlight heats up the gases. If the balloon needs to be lowered, the

white/light side of the balloon is rotated into the sun. The sunlight is reflected off the white

surface which stops the gases from expanding and makes the balloon lower itself. This is

essentially how the balloons are controlled in the upper atmosphere. It is assumed that the

Figure 1

balloon will cover the same diameter along the ground (40 Km) even if it changes its

position in height within the Stratosphere.

Because it is possible to control the positioning of one balloon against another, it is

therefore assumed that there will always be the same density of balloons over a given area.

Because New Zealand is surrounded by water, and is very thermally active due to its

position on a fault line, there are many islands in the surrounding waters that are classed as

part of New Zealand. Some of these include: The Chatham Islands, White Island, Stewart

Island etc. Because all of these islands are classed as New Zealand, it is important to

incorporate them under the balloons over New Zealand. When we calculated the area of

New Zealand with which the balloons had to cover, we included a small amount of

surrounding ocean so that all of the offshore islands

would have internet provided.

Using “Google Maps Area Calculator”, we calculated that

New Zealand (including the surrounding oceans and the

Chatham Islands) had an area of 417904.43km2. In the

photograph to the right, the area that was calculated is

shown. You can see that a small portion of ocean is also

included in our calculations. The area is shown in the

screen shot to the right. Area= 413351.65 Km2

The area for the Chatham islands is shown in the

screenshot below. Area=

4552.78Km2

The area of New Zealand (413351.65

Km2) + the area of the Chatham

Islands (4552.78Km2) equals the total

area of balloons needed to provide

complete internet coverage for the

whole of New Zealand = 417904.43

Km2.

When calculating the area that the balloons needed to cover, we

assumed that people would want to access the internet anywhere

in New Zealand so we didn’t neglect areas with low populations in

our calculation.

We were told that each

balloon covers a radius of 40

Km. We assume that this

means that the circular pattern the balloon covers has a

ground diameter of 40 kilometres; not the distance between the balloon and the ground

equalling 40m. (See figure 1)

The Loon:

The loon is a large balloon, (approx. 15m by 20m) which is filled with helium gas. The

balloon envelope is made of polyethylene sheets which is strong, allowing the balloon to

withstand the harsh conditions of the stratosphere.

Hanging under the balloon envelope is a small box which contains all the loon’s electronic

equipment. This includes circuit boards that control the system and radio antennas to communicate

with other balloons and with internet antennas on the ground and batteries for storing solar power

to be used at night. 1

The loon communicates with ground with a radio frequency of 2.4GHz and 5.8GHz. It connect with

antennas on the ground and then connects these antennas with a ground station which connects

them to an existing internet network. This is much like normal wireless networks, except it will allow

the internet to be transmitted much further and to much more isolated locations. The antenna is

connected to a consumer grade router which will provide that location with internet.

Our final answer is also based on the idea that every internet transmitting balloon is

working, and that every balloon’s electrical equipment is working to its full potential, and

delivering internet to people at a range of 40 m in diameter along the ground.

Calculations:

1 http://www.google.com/loon/how/#tab=equipment

Figure 2

Figure 2

Figure 2.1

A low density system can be created by having a 50% overlap of each balloon coverage area.

This creates an average of 1.5 balloons covering any one point on land.

In this diagram (figure2.1) there are:

- 4 ¼ of balloon coverage areas

- 6 ½ of balloon coverage areas

- 2 whole balloon coverage areas

4/4 + 6/2 +2

6 whole balloon coverage areas

Therefore for every 40 x 60km section of land, there are the equivalent of 6 balloons.

40 x 60 = 2400km2

Now to find the equivalent size of the area per balloon:

2400 ÷ 6 = 400km2 per balloon

Then to find the number of balloons needed to cover new Zealand, the total area of New

Zealand needs to be divided by the area per balloon:

417,904.43 ÷ 400 = 1044.761075

= 1045 balloons (4sf)

However due the urban areas needing a higher density of balloons, this low density would

only be to cover non-urban areas. Therefore the calculation would be the total area of non-

urban areas divided by the area per balloon.

- Urban areas = 5078km2

417,904.43 – 5078 = 412826km2

412826 ÷400 = 1032.065

= 1033 balloons (4sf)

Therefore 1033 balloons would be needed to cover non-urban areas.

This concentration of balloons in non-urban areas guarantees the coverage of internet for

everyone living in these areas.

As certain areas of the country, such as large urban environments, have higher population

densities than others, this would mean that the amount of balloons in these areas needed

to be increased. Having a larger amount of balloons over these particular areas would allow

for the wireless network to be more reliable and to accommodate the increased proposed

usage. The interconnected “mesh” of balloons over these areas would contain more

balloons within the same area as over the non-urban areas “to help meet the higher

bandwidth demands that are typical in urban areas, (therefore the) balloons may be

clustered more densely (over urban areas).” The amount of overlap in the urban areas will

also be increased substantially, from 50% of the ground area covered by each balloon to

75% overlap. The amount of land claimed to be “high density” by Statistics New Zealand was

deemed to be 5078 Km2 (approximately 1.9% of the total land area), so this was the figure

used in our calculations. By removing this value from our overall coverage area for the

greater New Zealand area and its dependants, as to avoid doubling up on land area covered

by any calculations, separate figures for both the “High” and “Low” density areas were able

to be calculated. Where any given point in non-urban areas would be covered by an average

of 1.5 balloons, the higher density areas would be covered by an average of 12. This will

allow the wireless network to meet any higher usage demands by ground users and allow

individual balloons to be less likely to reach their full bandwidth potential which would

produce less stress on their capacity to function and the network as a whole.

How the High Density area was calculated:

Figure 3.1

Figure 4

Figure 5

By having an array of circles with 75% overlap of radius (as shown in the diagram), the number of

balloons in the high density area could be calculated with respect to how much area the average

balloon covered.

As is shown on the diagram, there are

many different combination of how

different part of a circle can be a part

of this idealised part of a circle. In

order to calculate the number of

circles representing parts of coverage

for individual balloons, it was

necessary to calculate several

complicated areas of sectors of

circles.

For the calculation of the 1/16th of a

circle, where area q = area x + z,

Where radius of the circle = 20 km,

°

Using the calculator at planetcalc.com, the area of

segment z is 4.72 km2, and the chord length is 10.35 km.

See figure 4.

In order to find the length of the other 2 sides of the

isosceles triangle that encompasses x, we use the

hypotenuse of that triangle which was the chord length

we calculated before.

Using Pythagoras Theorem,

Finding the area of the triangle, and adding it to the value of z we found

earlier, we get the total area of q.

Which we calculated to be a proportion of 0.025 of the total circle’s area ( ).

Similar calculations were carried out for other proportions of the circle in various proportions.

Proportion of Circle Number of instances

Proportion of Whole Circle Totals:

1 1 1 1

1/4 4 0.1956 0.7824

1/4 4 0.25 1

1/16 4 0.025 0.1

3/16 8 0.1661 1.3288

3/4 4 0.8044 3.2176

9/16 4 0.6383 2.5532

1/8 8 0.0977 0.7816

3/8 8 0.4023 3.2184

1/2 4 0.5 2

TOTAL NUMBER: 15.982

The total number 15.982 was rounded to 16.

This value of 16 was then divided by the number of square kilometres represented in the original

diagram, namely 1600 km2. This gave us a value for the density of the high density balloon areas of 1

balloon per 100 square kilometres.

This concentration of balloons in urban areas guarantees the coverage of internet for

everyone living in these areas.

Based on the working shown in the previous paragraphs, we came to the conclusion that

1084 internet transmitting balloons would be needed to provide the whole of New Zealand

(including the surrounding islands) with internet access. This is the number of balloons that

would constantly need to be above our country, with higher densities of balloons over the

larger cities. As calculated in the low density calculations, 1033 balloons are needed to

provide for all of the rural areas in New Zealand. As calculated in the high density

calculations, 51 balloons were needed to cover all of the urban areas. This proves that we

will need 1084 balloons in total (1033 + 51).

Mathematical model of the situation in Excel: ( See Appendix)

The situation of the movement of the balloons can be modelled in excel. This can be done by finding

the x and y values of a balloon at a given time, and by then finding how they interact with each other

because of it.

The first thing to do was to set up a starting point for the balloons. This was done using the balloon

array that we decided would be used in the lower population density areas, namely with 1 balloon

per 400km2. In this system, there is a distance of 20 km between each balloon (assuming that the

balloons are in a square grid as explained above). Starting x and y for positions of balloons were

inputted into Excel to model ideal “starting positions”.

The next thing to do was to calculate the random component of the wind that would affect the

movement of the balloons. In order to do this, we calculated that after 15 minutes, assuming the

values for stratospheric wind given by Google2, the average balloon would have moved by ±8 km to

±32 km. Therefore, by simulating this random movement of the balloons, and calculating by how

much the balloons will “bounce back” due to their being likened to a spring3. In order to simulate

this, I used the following formula in Excel:

=(D13+INT(RAND()*(15)-8))

Where the simulated wind effects are assumed to give a random movement to the balloon, of

maximum magnitude 0.25 hours * 32 = km.

With D13 representing any x or y value relating to the position of one of the balloons (only in the

horizontal plane), thereby simulating the random wind that might affect the balloons in that 15

minute time period.

The next stage was to analyse the difference in values between multiple balloons.

=F16 + (0.5 * ((F16 - F18) + (F16 - F14)))

This formula means that in the y axis, the balloon moves slightly towards or away from the other 2

balloons in the y axis surrounding it, by calculating the difference between the values, summing

them, multiplying them by a half, and then adding these to the original value for the y position of the

balloon. The same is repeated for the x axis. This was repeated 3 times, the results of which are

demonstrated here for one of the experiments.

The result of this exercise was that there was not a significant change in the positions of the balloons

over time. Looking at the values that were generated in the third and final round of analysis after 45

minutes, the values are not too much different from the original values that were given, for

example, on the spreadsheet, balloon (5, 5) has changed its y position from the original 120 to 134.

Therefore, it can be said that the arrangement of the balloons that we decided upon for low

population density areas is good enough to allow for reliable coverage of low population areas in

this simulation. This represents a worst case scenario, in which the movement of the balloons is

completely random. In real life, the amount of adjustment of the balloons height would be much

more targeted, in that the knowledge of where the wind currents in the stratosphere are and which

altitude to move towards is known. Therefore, it can be said that our density of balloons in New

Zealand is appropriate for low population areas in order to provide reliable internet access.

2 www.google.com/loon 3 Patent - Relative Positioning of Balloons with Altitude Control and Wind Data US20130175391, 2c).

Figure 6

CONCLUSION:

Our calculations only included the use of area covered by the overlapping balloons which

incorporated the average amount of balloons covering a single

given point. This did not include the edges of the greater reception

area which would only have individual balloons that sit on the

exterior of the collective group connecting to the ground area,

which are only partly overlapped and therefore provide less

effective signalling to the surface beneath them. However, as we

considered the waters immediately surrounding New Zealand in

our calculations of the overall area that needed to be covered by

Project Loon, we already accounted for any usage on or just off the

shores of the country. Therefore, the areas with lower signal

strength from lack of overlapping balloon signals would hardly be

used anyway and would not cause a problem for any users off

shore. This extra area is also helpful in accounting for the

movement of the balloons due to wind, as they will be moved

around despite corrections done from ground bases and/or super

node balloons. Even though the main area of balloons we have

calculated may shift, there will still be a slightly larger amount of

signal surrounding that, albeit not as strong or reliable. Reference

Figure 6.

If we had had more time, we would have calculated the wind power, and how it would

change the distribution of the balloons over New Zealand. This would have given a more

accurate description of the coverage.

We would also investigate different models as to the different densities in different parts of

the country to accurately distribute the coverage according to the areas of higher/lower

internet usage.

We found that 1033 balloons for non-urban areas in New Zealand, and would need 51

balloons for urban areas. With more time, we could have separated these numbers into

more refined categories. But we found that in order to guarantee internet access to

everyone in New Zealand, our models would be sufficient, making the total number of

balloons needed 1084.

Balloon on X axis 1 2 3 4 5 6 7 8 9 10

x y x y x y x y x y x y x y x y x y x y

Balloon on Y axis:

1 0 180 20 180 40 180 60 180 80 180 100 180 120 180 140 180 160 180 180 180

Random Change 3 185 12 184 45 186 61 174 84 186 98 172 117 182 137 183 166 181 180 183

2 0 160 20 160 40 160 60 160 80 160 100 160 120 160 140 160 160 160 180 160

Random Change 2 160 21 161 33 155 63 153 76 162 102 153 117 160 142 161 160 165 176 157

3 0 140 20 140 40 140 60 140 80 140 100 140 120 140 140 140 160 140 180 140

Random Change -7 143 19 142 46 140 54 138 84 135 100 143 114 140 144 140 164 137 182 145

4 0 120 20 120 40 120 60 120 80 120 100 120 120 120 140 120 160 120 180 120

Random Change 4 121 22 114 41 123 54 112 85 114 103 125 116 122 143 114 160 116 181 126

5 0 100 20 100 40 100 60 100 80 100 100 100 120 100 140 100 160 100 180 100

Random Change -5 98 23 97 34 104 62 96 85 103 92 106 118 93 139 98 165 95 177 96

6 0 80 20 80 40 80 60 80 80 80 100 80 120 80 140 80 160 80 180 80

Random Change -7 85 24 76 44 82 63 76 86 73 98 84 112 81 138 85 155 86 185 85

7 0 60 20 60 40 60 60 60 80 60 100 60 120 60 140 60 160 60 180 60

Random Change -4 66 24 63 35 62 54 65 76 55 94 56 121 63 139 61 160 65 175 64

8 0 40 20 40 40 40 60 40 80 40 100 40 120 40 140 40 160 40 180 40

Random Change -4 34 17 45 40 45 56 35 86 45 106 34 118 33 139 42 163 34 182 42

9 0 20 20 20 40 20 60 20 80 20 100 20 120 20 140 20 160 20 180 20

Random Change -2 26 14 18 42 12 56 22 72 14 101 22 116 13 134 20 155 24 181 17

10 0 0 20 0 40 0 60 0 80 0 100 0 120 0 140 0 160 0 180 0

Random Change -3 -7 14 -6 40 -8 64 0 73 -1 101 -4 121 -5 134 -4 160 -7 174 -1

FIRST ANALYSIS AFTER 15 MINUTES

X Number

2 3 4 5 6 7 8 9

Y number x y x y x y x y x y x y x y x y

2 26.5 164.5 20.5 153 68.5 147.5 68 171 105 145 118.5 163 143.5 159.5 155 171

Random Change 28.5 156.5 24.5 146 64.5 141.5 63 172 110 144 111.5 162 149.5 164.5 147 177

3 16.5 142.5 55 140 49.5 138.5 87.5 129.5 97.5 148.5 111.5 138.5 145.5 141.5 168 131.5

Random Change 12.5 138.5 50 134 45.5 134.5 81.5 123.5 89.5 143.5 113.5 137.5 147.5 138.5 173 137.5

4 23 106 42 133 50 105.5 85.5 109.5 110 132 116 124.5 144.5 109 155.5 112

Random Change 28 110 45 132 48 111.5 88.5 105.5 114 126 115 118.5 143.5 101 159.5 114

5 23 93 25.5 111.5 65.5 88.5 84.5 105 83.5 114 122 84 137.5 102 172.5 93

Random Change 18 89 20.5 108.5 65.5 91.5 89.5 103 82.5 112 122 78 129.5 108 178.5 94

6 24.5 68.5 53.5 88 68 74.5 91.5 66 103 91 104.5 77.5 137 86.5 147.5 87

Random Change 16.5 64.5 53.5 92 64 75.5 93.5 60 104 85 97.5 77.5 143 79.5 147.5 82

7 27.5 62 28 60 48.5 71.5 66 49.5 86 53 127 67.5 139.5 58 161 67.5

Random Change 23.5 65 27 52 49.5 64.5 59 53.5 85 45 125 65.5 139.5 56 163 59.5

8 15 50.5 41.5 50 57 25 98 55.5 114.5 29 117.5 28 141.5 50.5 168.5 26

Random Change 19 50.5 33.5 49 56 25 104 61.5 118.5 24 110.5 27 139.5 52.5 173.5 22

9 12.5 17 44 4 52 31 64.5 6 98.5 30.5 112.5 5 131.5 21.5 148.5 29.5

Random Change 13.5 9 49 6 46 37 58.5 -2 102.5 32.5 114.5 6 128.5 19.5 153.5 22.5

SECOND ANALYSIS AFTER 30 MINUTES

X Number

2 3 4 5 6 7 8

Y number x y x y x y x y x y x y x y

3 65.25 131.5 34.75 140.25 87.25 108 67 156.5 113.75 134 148.5 139.5

Random Change 62.25 124.5 38.75 139.25 91.25 108 68 149.5 113.75 126 154.5 142.5

4 54.75 153.25 40.5 104.25 91.5 92.25 142 140 112.25 123.5 148.5 85.75

Random Change 52.75 152.25 42.5 100.25 89.5 96.25 146 139 106.25 125.5 146.5 82.75

5 -8.25 126.75 75 77.25 88 104.25 56 133.5 137.75 46 115.75 130

Random Change -4.25 132.75 78 71.25 84 103.25 58 129.5 132.75 51 116.75 134

6 83.25 114 70.5 75 112.75 39.75 124.25 101.25 71.5 72.75 151.5 79.25

Random Change 89.25 111 65.5 67 114.75 37.75 123.25 95.25 63.5 71.75 152.5 82.25

7 10.5 39.25 39 76.25 19.25 52.25 58.75 30.5 146 80.5 137.75 49.5

Random Change 14.5 43.25 31 77.25 19.25 45.25 61.75 22.5 147 85.5 136.75 45.5

8 29 60.25 64.25 -5.25 149.25 98.5 143.25 3.75 101.25 15.75 145 80.5

Random Change 31 62.25 65.25 -2.25 149.25 92.5 149.25 2.75 93.25 20.75 140 72.5

THIRD ANALYSIS AFTER 45 MINUTES

X Number

4 5 6 7

Y number x y x y x y x y

4 26.625 76.25 91.375 72.875 229 167.125 89.25 140.125

Random Change 28.625 70.25 88.375 77.875 228 170.125 90.25 135.125

5 102 24.5 65.875 106.125 -18.625 181.875 180.625 -29.75

Random Change 98 23.5 61.875 107.125 -17.625 186.875 177.625 -34.75

6 76.5 59.625 177.875 -5.625 186.625 135.75 -12.875 54.75

Random Change 77.5 63.625 171.875 0.375 180.625 138.75 -16.875 47.75

7 -3.375 110.25 -93.5 40.625 -12.75 -20.375 215.625 137

Random Change -10.375 103.25 -91.5 38.625 -19.75 -15.375 219.625 141

Bibliography:

Please Note: All sources were found and used on the 10th of August 2013.

Name: Project Loon

Last Updated: 09th August

Author: Wikipedia

URL: http://en.wikipedia.org/wiki/Project_Loon

Name: Area of New Zealand and Surrounding Islands

Author: Google Maps

URL: http://www.daftlogic.com/projects-google-maps-area-calculator-tool.htm

Appendix:

Name: Circular Segment Calculator

Author: PlanetCalc

URL: planetcalc.com/1421

Name: Statistics NZ pdf document

Author: Statistics NZ

New Zealand urban-rural profile report

URL: http://www.stats.govt.nz/~/media/Statistics/browse-categories/people-and-

communities/geographic-areas/urban-rural-profile/maps/nz-urban-rural-profile-

report.pdf

Name: Upper Troposphere and Lower Stratosphere

URL: http://www.google.com/patents/US8175332

Name: Loon for All

Author: Google

URL: http://www.google.com/loon/